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The WTO Trade Effect

Pao-li Chang, Myoung-jae Lee September 2007

Paper No. 06-2007

The WTO Trade Effect

Pao-Li Chang∗

School of Economics

Singapore Management University

Singapore 178903

Myoung-Jae Lee†

Department of Economics

Korea University

Seoul, Korea

September 23, 2007

Abstract

Rose (2004) showed that the WTO or its predecessor, the GATT, did not promote

trade, based on conventional econometric analysis of gravity-type equations of trade. We

argue that conclusions regarding the GATT/WTO trade effect based on gravity-type

equations are arbitrary and subject to parametric misspecifications. We propose us-

ing nonparametric matching methods to estimate the ‘treatment effect’ of GATT/WTO

membership, and permutation-based inferential procedures for assessing statistical sig-

nificance of the estimated effects. A sensitivity analysis following Rosenbaum (2002)

is then used to evaluate the sensitivity of our estimation results to potential selection

biases. Contrary to Rose (2004), we find the effect of GATT/WTO membership econom-

ically and statistically significant, and far greater than that of the Generalized System of

Preferences (GSP).

Keywords: GATT/WTO; GSP; treatment effect; matching; permutation test; signed-

rank test; sensitivity analysis

JEL classification: F13; F14; C14; C21; C23

∗Tel: +65-6828-0830; fax: +65-6828-0833. E-mail address: plchang@smu.edu.sg (P.-L. Chang).†Tel: +85-2-3163-4300; E-mail address: myoungjae@korea.ac.kr

1. INTRODUCTION

In the post war era, world merchandize trade volume grew at an exponential rate and at a rate

much higher than world merchandize output: while exports volume grew at an annual rate

of 6.2% during 1950-2005, production grew at only 3.8% (WTO, 2006, p. 27). This trend of

expanded trade concurred with the development of the multilateral trade institution. Since

the coming into effect of the General Agreement on Tariffs and Trade (GATT) in 1947,

the framework of trade agreements regulating trade policies has grown in coverage and in

depth over the decades, culminating with the establishment of the World Trade Organization

(WTO) in 1995. The number of countries choosing to join the GATT/WTO also saw a steady

increase from the original 23 contracting parties to the current 151 members. By contrasting

the post-war phenomenon with the pre-war experience in the late 1920’s to 1930’s during

which the world trade volume fell into a downward spiral with uncontrolled tariff retaliations

among countries, it is natural for one to conclude that the GATT/WTO likely has spurred

the integration and expansion of world trade.

On theoretical grounds, several economic theories have also been proposed that explain

the mechanism of multilateral trade agreements in promoting trade. Major explanations

include the terms-of-trade argument and the political-commitment argument. On one hand,

multilateral trade agreements may help coordinate countries’ trade policies and prevent them

from engaging in the terms-of-trade-driven tariff retaliations which decrease trade volumes

(Johnson, 1953–1954; Bagwell and Staiger, 1999, 2001). On the other hand, multilateral

trade agreements may also help national governments to commit to liberalizing trade policies,

given the retaliation threat from other countries if the commitment is not carried out. This

enhances policy credibility with respect to domestic private sectors and brings about efficient

production and trade structure (Staiger and Tabellini, 1987, 1989, 1999). Other potential

mechanisms of GATT/WTO in encouraging trade often cited by economists or policymakers

also include the reduced uncertainty of member countries’ trade policies and overall business

environment, facilitated by binding tariffs or the GATT/WTO dispute settlement mechanism

(Evenett and Braga, 2005).

In view of the empirical observations and theoretical validation, it is thus surprising that

some recent studies showed that the GATT/WTO did not appear to have promoted trade.

Perhaps the most important and widely cited study is Rose (2004). The study uses a large

panel of data on bilateral trade for 178 trading entities during year 1948 to 1999, and conducts

conventional econometric analysis based on the gravity model of trade (which postulates that

bilateral trade depends log-linearly on the distance between two countries and their GDP’s,

and other determinants possibly affecting bilateral trade). The mechanism of GATT/WTO

in influencing trade is incorporated in the framework by two dummy variables, which indicate

respectively whether or not both countries are GATT/WTO members and whether or not

only one country is a GATT/WTO member. The coefficients on both dummy variables were

found in Rose (2004) to be insignificantly different from zeros, in the benchmark model with

ordinary-least-squares (OLS) regression, as well as in most subsequent sensitivity analysis

with variations in estimation methods and in the data.

Gravity-type models of trade have in recent years become popular in empirical studies

of bilateral trade pattern. Although the basic formulation can be justified by theories as in

Anderson (1979), Helpman and Krugman (1985), Deardorff (1998), and Anderson and van

Wincoop (2003), the augmented version of gravity equation adopted in Rose (2004) (and

in many other empirical studies) is often not. Various ad hoc regressors in addition to the

basic gravity variables (the distance and the GDP’s) are often added to the equation to

suit the purpose of the study without rigorous theoretical justifications. For example, the

survey by Oguledo and MacPhee (1994) cited 49 explanatory variables that had been used

in gravity-type empirical studies. Although the extra variables typically used to measure the

degree of trade frictions across countries (such as language barrier and colonial relationship)

might well have an impact on bilateral trade flows, it is not clear in what functional form

they would enter the basic gravity equation and how they would interact with one another.

To illustrate this point, we show in the main text that the main gravity equation of Rose

(2004) is misspecified by omitting higher-order interaction terms among regressors. Given

this, it is possible to construct richer parametric forms of specifications and find favorable

evidences of GATT/WTO’s trade-creating effect. We provide one such example in the main

text. However, without theoretical guidance, an investigation of this kind looks endless and

any conclusion drawn would seem arbitrary.

In this paper, we propose using nonparametric ‘matching’ methods to estimate the trade

effect of GATT/WTO membership. Nonparametric estimation does not assume knowledge

of the underlying true model and avoids potential biases stemming from parametric misspec-

ifications. If the gravity equation specified in Rose (2004) is indeed the correct underlying

model, using a nonparametric approach should lead to similar estimation results. Among

many possible nonparametric approaches to evaluating the ‘treatment’ effect of a policy or

program, matching method is relatively straightforward to implement. Matching is widely

used in the fields of labor and health economics. See, for example, Heckman et al. (1997),

Imbens (2004), and Lee (2005), and applications in Heckman et al. (1998), Lechner (2000),

Lee et al. (2007), and Lu et al. (2001).

Applying the terminology in the matching literature to our current context, the state of

both countries being GATT/WTO members is a ‘treatment’, and the country-couple in the

state is a ‘treated’ subject, in contrast with a ‘control’ subject where the two countries are

nonmembers. In essence, a pair-matching method compares the ‘responses’ (trade flows) of a

treated subject and a control subject who differ in their treatments but are otherwise similar

in every aspect likely to influence the bilateral trade flows. The difference in their bilateral

trade flows is then attributed to the treatment effect of both countries being GATT/WTO

members. Similar procedures apply if we want to estimate the effect of other treatments

such as only one country in a country-couple being a GATT/WTO member versus both of

them nonmembers. In finding the best match from the control group for a treated subject,

a list of covariates need to be identified in terms of which the similarity between any two

subjects is measured. For this, we use the same set of covariates as in Rose (2004). By using

the matching method, however, we do not assume any particular functional form that relates

these covariates to bilateral trade.

To assess the statistical significance of the treatment effect estimated by the matching

method, we propose using the permutation test. Although matching estimators are popular

in practice, asymptotic theories on their large sample properties are not fully established for

most data generating processes. See Abadie and Imbens (2006) for a large sample theory of

the matching estimator for independent observations. In practice, a standard t-statistic or a

bootstrap procedure is often used to derive the p-value or confidence intervals. Standard t-

statistic is straightforward but without theoretical justifications; bootstrap is computationally

demanding and argued by Abadie and Imbens (2006) to be invalid. In contrast with the above

asymptotics-based tests, the permutation test is an exact inferential procedure conditional on

the observed data. Under the null hypothesis of no treatment effect, two subjects in a matched

pair are ‘exchangeable’ in the labeling of their treatment status (treated or untreated). By

obtaining all possible permutations of the treatment labels in all pairs, the exact p-value of

the observed matching estimator can be computed by placing it in the distribution of the

permutations. See Pesarin (2001) and Good (2004) for an introduction to the concept, and

Ernst (2004) for a survey of the permutation method in general contexts. Recently, Imbens

and Rosenbaum (2005) showed that confidence intervals constructed by the permutation

method are far more reliable than other confidence intervals.

In applying the matching estimator and the permutation test, there are two potential

shortcomings. First, the matching estimator is susceptible to outliers (as OLS is). Second,

the permutation test is only ‘conditionally distribution-free’ — conditional on the sample at

hand; thus its finding is only valid within the sample. To provide more robust findings, we

also conduct the Wilcoxon (1945) signed-rank test version of the matching estimator and the

permutation test. Instead of the actual numerical differences, the ranks of the differences are

used in determining the distribution of the signed-rank test statistic across all permutations.

In addition to being robust to outliers, the signed-rank test turns out to be distribution-free,

so that findings based on this test are also valid out of sample.

Some country-couples may be more likely to join the GATT/WTO and also to experience

higher bilateral trade volumes, leading to a potential upward bias in the treatment effect

estimator. This selection-bias problem is relevant in both the parametric setting of Rose

(2004) and the nonparametric setting of ours. Selection on observable variables does not pose

a selection-bias problem. If, however, the selection is made based on unobservables that affect

both trade flows and the decision to join the GATT/WTO, then there is a selection problem.

We conduct a sensitivity analysis following Rosenbaum (2002) to evaluate the sensitivity of

our conclusions obtained under the assumption of no selection bias. This method examines

how severe the unobserved selection problem must be to overturn the original finding. A

finding is deemed robust if it takes a substantial difference between the treated and the

untreated in their odds of taking treatment (after controlling for the observable variables) to

overturn the finding. The use of similar sensitivity analysis is slowly increasing in numbers.

See, for example, Aakvik (2001), Imbens (2003), Hujer et al. (2004), Altonji et al. (2005),

and Lee et al. (2007), among others.

As another way to deal with the selection problem, we also apply the matching procedure

introduced above in restricted manners, where the potential matches for a treated subject is

limited to a certain subset of controls. They are: matching restricted to the observations of

the same country-couple, matching restricted to the observations in the same year, matching

restricted to the observations in the same GATT/WTO period, and matching restricted to

the observations of the same income-class combination. For example, there may be some

unobserved country-couple specific characteristics that affect both their GATT/WTO mem-

berships and their bilateral trade flows, and the characteristics may be systematically different

across country-couples. In this case, matching without restriction leads to a biased estimate

that contains the true treatment effect and the effect arising from the difference in unobserved

country-couple characteristics if the pair in a match are of different country-couples. The

bias is eliminated by restricting matching to the observations of the same country-couple.

Our nonparametric matching method and permutation-based inference procedures led to

findings opposite to Rose’s (2004): in short, we found economically and statistically significant

trade-promoting effect of the multilateral trade institution. The bilateral trade between

two countries is higher by 193% for country-couples who are both GATT/WTO members,

relative to their counterparts who are both nonmembers. The effect is similar if estimation

is restricted to cross-section variation (in the case of matching within the same year or

the same GATT/WTO period). On the other hand, when estimation is restricted to time-

series variation (in the case of matching within the same country-couple), the bilateral trade

increases by a factor of 126% when a country-couple are both GATT/WTO members, relative

to when they both are not. Both estimates are robust to a reasonable degree of potential

selection biases. In his findings, Rose (2004) also suggested that the Generalized System of

Preferences (GSP) had a significant and larger effect than GATT/WTO. In contrast, GSP is

found in our analysis to raise bilateral trade volume, but by a factor smaller than the effect

of ‘both in GATT/WTO’, regardless of the matching criteria. Based on matching restricted

to country-couples of the same income-class combination, bilateral trade is estimated to be

higher by a factor of 73% for a trading relationship that extends the GSP scheme, relative

to its counterpart that does not.

The findings of Rose (2004) were also challenged by two other studies. On one hand,

Tomz et al. (2005) highlight the effective participation of nonmember participants in the

GATT/WTO system. These include colonies, de facto members, and provisional members,

who enjoy to a large extent the same set of rights and obligations under the agreement as

formal members. By simply re-classifying these countries as de facto GATT/WTO members

without changing the estimation framework of Rose (2004), Tomz et al. (2005) find that

GATT/WTO substantially increases trade and that its effects are relatively stable across

countries and over time. Subramanian and Wei (2007), on the other hand, emphasize asym-

metries of GATT/WTO trade effects across different sub-samples—developed versus develop-

ing countries, old versus new developing countries, and generally unprotected sectors versus

protected sectors. They find that the GATT/WTO institution promotes trade when and

where the multilateral trade agreements are in full force. In contrast with these two papers,

we do not attempt to refine the data of Rose (2004) or to differentiate the trade effects among

sub-samples. Instead, our paper focuses on the improvement of estimation and inferential

methodologies as introduced above.

The rest of this paper is organized as follows. In Section 2, we highlight possible mis-

specifications of the Rose (2004) gravity equation and arbitrariness of conclusions derived

from the parametric framework regarding the GATT/WTO effect. We then introduce the

nonparametric matching methodology and permutation-based inference procedures in Sec-

tion 3. Section 4 reviews the data set of Rose (2004). Our estimation results and findings

are reported in Section 5. Section 6 concludes.

2. MISSPECIFICATION OF THE GRAVITY EQUATION

In this section, we illustrate the potential misspecification of the main gravity equation used

in Rose (2004) and the arbitrariness of conclusions derived based on variations of the model.

The benchmark result of Rose (2004) based on an OLS regression of a gravity-type equation

is replicated in Column (I) of Table 1.1 As shown, the coefficients of the two GATT/WTO

dummy variables (Both in and One in) are insignificantly different from zeros.

In Column (II), we run a misspecification test of the gravity equation (I). For this, we

apply the regression equation specification error test (RESET) of Ramsey (1969), which

tests whether non-linear combinations of the regressors have any power in explaining the

regressand. If yes, then the original model is misspecified. The test is done by augmenting

the original regression equation with the square or higher powers of the predicted value of the

regressand from the original regression and testing the significance of the coefficients of these

augmented terms. As indicated in Column (II), the coefficient of the squared predicted value

y2 of the log real trade derived from the gravity equation (I) is significant. This indicates that

the original gravity equation is misspecified by omitting interaction terms among regressors1The data set used is Rose’s (2004) downloaded from his website. More details on the data set are discussed

in Section 4.

or squares of regressors, because y2 is a sum of these terms.

Given the finding of the RESET test, we experiment with augmenting the gravity equa-

tion (I) with interaction terms among the two GATT/WTO dummy variables and the other

regressors, and rerun the regression. The results in Column (III) show that many interaction

terms are significant, illustrating clearly that the benchmark model of Rose (2004) is mis-

specified.2 With the interaction terms in, the effects of GATT/WTO membership for trading

partners i and j in year t are,

{Both in effect}ijt = β{Both in} + β{Both in x GSP}{GSP}ijt + . . .

+ β{Both in x Ever colony}{Ever colony}ijt;

{One in effect}ijt = β{One in} + β{One in x GSP}{GSP}ijt + . . .

+ β{One in x Common colonizer}{Common colonizer}ijt

+ β{One in x Ever colony}{Ever colony}ijt,

where β is the coefficient of the corresponding regressor or interaction term. These effects

vary across trading partners and years ijt, and Table 2 shows some quantiles of these effects.

As shown in Table 2, the mean effect of GATT/WTO membership for the whole sample based

on the specification in (III), obtained by replacing the regressors with the sample means and

β with the estimate, is significant and positive.

Of course, the specification in (III) is just one of many possibilities to allow higher-

order parametric specifications of bilateral trade. One can conjecture that possibly richer

parametric forms of specifications may lead to even more favorable evidence of GATT/WTO

effect. However, without theoretical guidance, an investigation of this kind looks endless and

any conclusion drawn would seem arbitrary.

In the following, we resort to the nonparametric matching approach to the estimation of

the GATT/WTO trade effect. The approach requires identification of the covariates that are

likely to have affected bilateral trade, for which we will adopt the same set of covariates as

in Rose (2004). However, beyond that, no previous knowledge about the underlying model

structure is required: estimation and inference are derived without having to specify the2The null hypothesis that all interaction terms in parametric specification (III) are irrelevant can be easily

rejected by the χ2-test: [(R2a−R2

0)/(1−R2a)]∗(N−k), where R2

a (respectively R20) is the R2 under specification

(III) (respectively (I)), N is the sample size, and k is the number of regressors under specification (III). Thetiny difference in R2 between parametric specifications (I) and (III) is magnified by N − k; as the currentsample size is huge, we get significant interaction terms in spite of little change in the goodness-of-fit.

functional form that relates the bilateral trade pattern to the covariates; thus, all forms

of higher-order or interaction terms of the covariates are accommodated. This avoids the

often large variation in estimates across different functional forms and parametric modeling

assumptions, and as a result, the biases stemming from model misspecifications.

3. METHODOLOGY

Suppose there are N countries in the world. With the countries indexed by i = 1, ..., N , let

yijt be the logarithm of the real bilateral trade volume between countries i and j in year

t. Define xijt as a vector of covariates, which includes mainly the characteristics of country

couple (i, j) in year t. For country couple (i, j), two effects are of interest:

• the effect when both countries are in the GATT/WTO, relative to when none is in.

• the effect when only one country is in the GATT/WTO, relative to when none is in.

We will also investigate the effect of GSP on bilateral trade, which is:

• the effect when one country is a GSP beneficiary of the other country or vice versa,

relative to the scenario of no GSP.

To facilitate exposition, focus on both-in versus none-in, and define

dijt = 1 if both in and 0 if none in.

The analysis for the effect of one-in or GSP is analogous. Thus, the data consists of

zijt = (dijt, x′ijt, yijt)′, i = 1, . . . , N , j = i + 1, . . . , N , and t = 1, . . . , T . In the terminology of

the matching literature, yijt is a response variable, the observations with dijt = 1 constitute

the treatment group, and those with dijt = 0 the control group. Note that we will use the

word ‘couple’ (an observation unit which comprises two countries between which trade volume

is concerned) and ‘pair’ (two observation units which are considered a match) separately to

avoid confusion with the matching literature.

3.1 Mean Effects and Matching

Define two ‘potential’ response variables:

y1ijt : potential treated response for couple (i, j) in year t,

y0ijt : potential untreated response for couple (i, j) in year t.

We will denote ‘couple (i, j) in year t’ simply ’subject ijt’ from now on. The subject-ijt

treatment effect is y1ijt − y0

ijt, which is, however, not identified. Instead, usually one tries

to estimate the mean effect E(y1ijt − y0

ijt). Omitting the subscripts to simplify exposition,

E(y1 − y0) is identified by the group mean difference

E(y|d = 1)− E(y|d = 0) = E(y1|d = 1)−E(y0|d = 0) = E(y1 − y0) if (y0, y1)q d

where ‘q’ stands for statistical independence. If we have only y0 q d, then

E(y|d = 1)− E(y|d = 0) = E(y1|d = 1)− E(y0|d = 0) = E(y1|d = 1)−E(y0|d = 1)

= E(y1 − y0|d = 1) which is the ‘effect on the treated ’.

Analogously, if y1 q d, then

E(y|d = 1)− E(y|d = 0) = E(y1 − y0|d = 0), which is the ‘effect on the untreated ’.

Since y0 is the control response, in general, y0 q d is more plausible than y1 q d.

For the GATT/WTO effect, both the effect on the treated (i.e., those who chose to join

GATT/WTO) as well as the effect on the untreated (i.e., those who chose not to join) are of

interest. Since

E(y1 − y0) = E(y1 − y0|d = 0)P (d = 0) + E(y1 − y0|d = 1)P (d = 1),

if the effect on the treated is the same as the effect on the untreated, then both equal

E(y1−y0). Otherwise, the representative effect E(y1−y0) is a weighted average of the effect

on the treated and the effect on the untreated.

In observational data, the treatment and control groups usually differ in observed (xijt) or

unobserved variables (εijt). Matching removes the observed difference (and the unobserved

difference to the extent the two differences are related). In terms of equations, matching is

expressed by including x in the conditioning set in the preceding equations. The above group

mean difference equation becomes

and the E(y1 − y0)-decomposition equation becomes

Once the x-conditional effect is found, x can be integrated out to yield a marginal effect;

here, the integration can be done with different integrators (i.e., weighting functions). For

the effect on the treated, the distribution of x|d = 1 is typically used to render

E(y1 − y0|d = 1) =∫

E(y1 − y0|d = 1, x)dF (x|d = 1)

where F (·|d = 1) denotes the distribution of x|d = 1.

The assumption (y0, y1)qd|x states that y0 and y1 may be related to d but only through

x. This is nothing but a ‘no-selection bias’ assumption, which may be called ‘randomization

of d given x’. In the current context of bilateral trade, this assumption implies that a

treated subject and an untreated subject be comparable in terms of their potential trade

performance and likelihood of joining the GATT/WTO, if they exhibit the same observable

characteristics x. Thus, the observed untreated response of the untreated subject can be used

as a proxy for the counterfactual potential untreated response of the treated subject, and the

observed treated response of the treated subject a proxy for the counterfactual potential

treated response of the untreated subject.

If we are only concerned with the effect on the treated, E(y1 − y0|d = 1), the required

assumption, y0 q d|x, is weaker and requires only that a treated subject and an untreated

subject be comparable in terms of their potential untreated trade performance and likelihood

of joining the GATT/WTO, if they exhibit the same observable characteristics x. Again,

this implies that the observed untreated response of the untreated subject can be used as a

proxy for the counterfactual potential untreated response of the treated subject. The mean

effect on the treated can then be estimated based on the subset of the sample who receive the

treatment. The opposite is true if we are only concerned with the effect on the untreated.

Thus, the assumption for matching to work in essence requires that there be no systematic

unobserved difference across the treatment and control group that affects their potential

(treated or untreated or both) trade volumes and GATT/WTO member status. If there is

an unobserved variable ε that affects both d and (y0, y1), then there is a selection problem

and ε causes a bias—called ‘hidden bias’. Exactly for the unknown nature of the treatment

effect and its unknown dependence on the unobserved characteristics, in general, it is more

plausible for the assumption y0 q d|x to hold than y1 q d|x. Thus, in the empirical section,

we will place more emphasis on the estimation result of the effect on the treated than either

the effect on the untreated or the mean effect for the whole sample. While any effect of x

on (y0, y1) and d is dealt with by matching, there is no good way to deal with ε, for it is

unobserved. Nevertheless, a sensitivity analysis can be conducted to account for the presence

of ε and the extent it influences d and (y0, y1) as to be shown later.

So far, we introduced the basics of the treatment effect framework and matching concept.

In practice, matching for the effect on the treated proceeds in the following steps (the effect

on the untreated can be handled analogously). First, a treated unit, say unit ijt, is selected.

Second, control units are selected who are the closest to the treated unit ijt in terms of x.

If only one unit is selected, we get a ‘pair-matching’; otherwise, multiple-matching, in which

the number of matched controls may be allowed to be random or fixed. Third, assuming pair-

matching, suppose there are M pairs (where M corresponds to the number of the successfully

matched treated subjects), and ym1 and ym2 are the responses of the two subjects in pair

m ordered such that ym1 > ym2 without loss of generality; drop any pair with ym1 = ym2.

Then, defining

sm = 1 if the first subject in pair m is treated and − 1 otherwise,

the effect on the treated can be estimated with a pair-matching estimator

D ≡ 1M

sm(ym1 − ym2) →p E(y1 − y0|d = 1) under y0 q d|x,

which is simply the average of the difference between the treated response and the untreated

response across the M pairs of match.

Some remarks are in order. First, the matching scheme can be reversed to result in an

estimator for the effect on the untreated: a control unit is selected first and then a matched

unit from the treatment group later. Second, the distance ‖xijt − xi′j′t′‖ between two units

ijt and i′j′t′ in terms of x should be chosen; e.g., a scale-normalized distance between xijt

and xi′j′t′ , or alternatively, (xijt − xi′j′t′)′X−1

N (xijt − xi′j′t′) can be used, where XN is the

sample variance matrix in the pooled sample. Third, for a treated unit, if there is no good

matched control, then the unit may be passed over; i.e., a ‘caliper’ c may be set such that a

treated unit with

mini′j′t′∈C

‖xijt − xi′j′t′‖ > c, where ‘i′j′t′ ∈ C’ means unit i′j′t′ in the control group C,

is discarded. The number of matched pairs M used in the matching estimator D decreases

accordingly. For more discussions on treatment effect and matching in general, see, for

example, Rosenbaum (2002) and Lee (2005).

3.2 Permutation Test for Matched Pairs

Suppose that matching has been done resulting in M pairs, and that the two subjects are

exchangeable under the null hypothesis H0 of no effect: the joint distribution of the two

responses in each matched pair does not change when the two responses are switched. That is,

exchangeability is taken as the definition of ‘no effect’, which is weaker than the subject-wise

no-effect concept y1ijt−y0

ijt = 0, but stronger than the mean zero-effect concept E(y1ijt−y0

ijt) =

0. Exchangeability implies that, given the data, all 2M possibilities to permute two responses

in each pair are all equally likely with probability 2−M in the ‘permutation sample space’

with the 2M elements (equivalently, if they are not equally likely, then exchangeability does

not hold). Here, permuting two responses is equivalent to assigning one response to the

treatment group and the other to the control group.

Permutation inference is an exact inferential procedure conditional on all observed data.

Whether H0 is rejected or not depends on how extreme D is—i.e., the p-value of D. In

theory, this can be computed exactly as

1[Dk > D] if the H0-rejection region is in the upper tail

where Dk is a “D-like” effect estimator under permutation k. In practice, however, finding

the p-value this way tends to be too time-consuming. Instead, we will apply the following

sequence of approximations.

Generate M iid random variables wm, m = 1, ..., M , with P (wm = 1) = P (wm = −1) =

0.5. If wm = −1, the two responses in pair m are switched (the treated response assigned to

the control group, and the untreated response to the treatment group); otherwise, the two

responses in pair m are not switched. For pseudo sample k obtained this way, obtain the

pseudo effect estimator

D′k ≡

wmsm(ym1 − ym2)

where only wm’s are random. The p-value of D is then

1[D′k > D] if the H0-rejection region is in the upper tail,

where K is a number much smaller than 2M , say K = 1000. In principle, a pseudo sample

should not be repeated: ‘sampling from the 2M possibilities without replacement’ is required.

In practice, the chance of a pseudo sample being repeated in K (= 1000) pseudo samples is

negligible and can be ignored.3

A further simplification is possible by applying the central limit theorem (CLT) to wm’s.

Observe

E(D′k) = 0 and V (D′

k) = E(D′2k ) =

E{w2ms2

m(ym1−ym2)2} =∑M

m=1(ym1 − ym2)2

When M is large, the normally approximated p-value of D is

P (D′k > D) = P{ D′

{∑Mm=1(ym1 − ym2)2/M2}1/2

= P{N(0, 1) >D

{∑Mm=1(ym1 − ym2)2/M2}1/2

if the H0-rejection region is in the upper tail. Using this normal approximation, one does not

even have to simulate wm’s.

As is well known, we can obtain a confidence interval (CI) by “inverting” the test pro-3The proof is available from the authors upon request.

cedure. For instance, suppose that the treatment effect is the same for all pairs: the effect

increases the treated response by a constant, say β. In this case, replace ym1 with ym1 − β

when sm = 1 or ym2 with ym2 − β when sm = −1 to obtain

Dβ ≡ 1M

sm(ym1 − smβ − ym2)

and restore the no-effect situation. Define accordingly

D′β ≡

wmsm(ym1 − smβ − ym2)

to observe

E(D′β) = 0 and V (D′

β) = E(D′2β ) =

∑Mm=1(ym1 − smβ − ym2)2

Now conduct level-α tests with

{∑Mm=1(ym1 − smβ − ym2)2/M2}1/2

as β varies. The collection of β values that are not rejected is the (1 − α)100% confidence

interval for β.

See Martiz (1995), Hollander and Wolfe (1999), and Lehmann and Romano (2005) among

many others, for more on permutation (or randomization) tests in general. The use of

permutation-based tests, in stead of asymptotic tests, is especially convenient in the cur-

rent context with a panel of bilateral trade data, which possibly have a complicated data

structure with serial and spatial dependence, rendering the derivation of the asymptotic dis-

tribution of the matching estimator difficult. Based on the principle of exchangeability, the

permutation test requires the joint distribution of the treated and untreated responses to

remain the same despite the permutation. If the joint distribution is normal, this holds if

the x-conditional variances of the two responses are the same under the null of no effect.

This allows for any form of correlation between a treated response and an untreated response

in any matched pair and across matched pairs, and any form of heteroskedasticity across

matched pairs, thus accommodating a wide range of data structure.

3.3 Signed-Rank Test for Matched Pairs

The preceding permutation test has two potential shortcomings. One is its susceptibility to

outliers in x and y. The other is that the test is only ‘conditionally distribution-free’—the

permutation distribution under the null hypothesis is conditional on (x′, y, d), which enters

the variance V (D′k). Due to this conditioning, any finding from the test is applicable only to

the sample at hand. That is, the finding has ‘internal validity’, but not ‘external validity’.

If a test is distribution-free, then the finding holds unconditionally as well, which accords

external validity. A well known test that is robust and distribution-free is the Wilcoxon

(1945) signed-rank test. Applying this test to the current matching context, rank |ym1−ym2|,m = 1, ...,M , to denote the resulting ranks as r1, ..., rM . For instance, when M = 3,

|y11 − y12| = 0.3, |y21 − y22| = 0.09, |y31 − y32| = 0.21 =⇒ r1 = 3, r2 = 1, r3 = 2.

The signed-rank test statistic is the sum of the ranks for the pairs where the treated subject

has the higher response:

R ≡M∑

rm1[sm(ym1 − ym2) > 0] =M∑

rm1[sm = 1].

Thus, instead of actual numerical differences, the ranks of the differences are used in con-

structing the signed-rank R statistic, rendering it more robust to outliers than the estimator

The inference based on the signed-rank R statistic can similarly follow the permutation

inferential procedure. The permutated version R′ for R is

R′ ≡M∑

rm1[wmsm(ym1 − ym2) > 0] =M∑

rm1[wmsm > 0]

rm(1[wm = 1, sm = 1] + 1[wm = −1, sm = −1]).

Observe

E(1[wm = 1, sm = 1] + 1[wm = −1, sm = −1]) =1[sm = 1]

1[sm = −1]2

V (1[wm = 1, sm = 1] + 1[wm = −1, sm = −1]) =14.

Hence, because rm’s are fixed, under the H0,

E(R′) =M∑

rm =M(M + 1)

V (R′) =M∑

M(M + 1)(2M + 1)24

When M is large, the null distribution of {R′ − E(R′)}/SD(R′) can be approximated by

N(0, 1). The normally approximated p-value for R is

P{N(0, 1) >R − M(M + 1)/4

{M(M + 1)(2M + 1)/24}1/2}.

This test is distribution-free as (x′, y, d) does not appear in the mean or variance of the null

distribution.

The CI’s for the treatment effect can be similarly obtained by inverting the test. Conduct

level-α tests with different values of β using

Rβ − M(M + 1)/4{M(M + 1)(2M + 1)/24}1/2

, where Rβ ≡M∑

rmβ1[sm(ym1 − smβ − ym2) > 0]

and rmβ is the rank of |ym1 − smβ − ym2|, m = 1, ..., M .

In contrast to the confidence interval obtained based on Dβ with its point effect estimator

D, there is no point effect estimator available in the signed-rank test. As a point estimator,

one may take the Hodges and Lehmann (1963) estimator, which is obtained by solving for β

such that

Rβ =M(M + 1)

4{= E(R′)}.

That is, after transforming the data with the effect estimate β, one obtains a transformed

signed-rank statistic Rβ that coincides with the mean of the statistic under the null.

3.4 Sensitivity Analysis with Signed-Rank Test

So far the unobserved differences between two subjects in a matched pair have been ignored.

Rosenbaum (2002) presents a sensitivity analysis to account for an unobserved confounder

ε that might affect d. Since our data set is observational where countries self-select the

treatment, there may be unobserved differences across the treatment and control groups,

causing a hidden bias (or selection bias). Besides, not all country-couples are observed at all

years; this is a missing variable problem, which is also a selection problem. Hence it matters

to allow for selection problems.

When two subjects in a given pair differ in ε that influences d, their relative probabilities

of receiving the treatment are no longer the same. Rosenbaum (2002) assumes

1Γ≤ odds of one subject being treated

odds of the other being treated≤ Γ, for some constant Γ ≥ 1 ∀ pair.

For instance, if the first subject’s probability of receiving the treatment is 0.6 (0.6) and the

second subject’s probability is 0.5 (0.4), then the odds ratio is

0.6/0.40.5/0.5

= 1.5 (0.6/0.40.4/0.6

= 2.25).

The sensitivity analysis goes as follows. Initially, one proceeds under the assumption of no

unobserved difference (Γ = 1). Then Γ is increased from 1 to see how the initial conclusion is

affected. If it takes a large value of Γ to reverse the initial finding, i.e., if only a strong presence

of ε can overturn the initial conclusion, then the initial conclusion is deemed insensitive to ε.

Otherwise, if it takes only a small value of Γ, then the initial finding is deemed sensitive.

The question is then how “large” is large for Γ. Suppose Γ = 2.25 and imagine that ε

were observed. By observing ε, one would be able to tell who is more likely to be treated

between the two subjects and ask whether the probability difference results in as much as an

odds ratio of 2.25? If the answer is no, Γ = 2.25 is a large value. Thus how large is large

for Γ depends on what is included in x. If most relevant variables are in x and thus if it is

hard to think of any important omitted variable in ε, then even a small value of Γ may be

regarded as large.

An easy-to-implement sensitivity analysis is available for the signed-rank test. Define

p+ ≡ Γ1 + Γ

≥ 0.5 and p− ≡ 11 + Γ

≤ 0.5.

Further define R+ (R−) as the sum of M -many independent random variables where the mth

variable takes rm with probability p+ (p−) and 0 with probability 1− p+ (1− p−). Writing

R+ as∑M

m=1 rmum, where P (um = 1) = p+ and P (um = 0) = 1− p+, we get

E(R+) =M∑

rmE(um) = p+M∑

rm =p+M(M + 1)

V (R+) =M∑

r2mV (um) = p+(1− p+)

p+(1− p+)M(M + 1)(2M + 1)6

Doing analogously, we obtain

E(R−) =p−M(M + 1)

2and V (R−) =

p−(1− p−)M(M + 1)(2M + 1)6

The means and variances with p+ and p− include E(R′) and V (R′) as a special case when

p+ = p− = 1/2.

Suppose that the H0-rejection interval is in the upper tail. Rosenbaum (2002, p.111)

shows that

P (R+ ≥ a) ≥ P (R′ ≥ a) ≥ P (R− ≥ a).

Using these bounds, the p-value obtained under no hidden bias can be bounded by P (R+ ≥ a)

in case of rejection.4 Specifically, suppose that the H0-rejection interval is in the upper tail,

and the no-hidden-bias p-value is

P{N(0, 1) ≥ R− E(R′)SD(R′)

} = 0.001,

leading to the rejection of H0 at level α > 0.001. Rewrite P (R+ ≥ a) ≥ P (R′ ≥ a) as

P{R+ −E(R+)SD(R+)

≥ a− E(R+)SD(R+)

} ≥ P{R′ −E(R′)SD(R′)

≥ a− E(R′)SD(R′)

' P{N(0, 1) ≥ a− E(R+)SD(R+)

} ≥ P{N(0, 1) ≥ a− E(R′)SD(R′)

Replacing a in the above equation with the realized R gives the p-value of R on the right

hand side and its bound on the left hand side. The left-hand side can be obtained for different4In case of acceptance, P (R− ≥ a) shows the possibility of rejection when ε is taken into account. For a

two-sided test, the p-value gets multiplied by 2. For a lower-tail test, subtracting the last display from 1 toget

1− P (R+ ≥ a) ≤ 1− P (R′ ≥ a) ≤ 1− P (R− ≥ a) =⇒ P (R+ < a) ≤ P (R′ < a) ≤ P (R− < a),

which can be used for bounds.

values of Γ. Then find, at which values of Γ, the upper bound crosses the level α. If this

happens at, say Γ = 2, then check whether or not Γ = 2 is a large value. If Γ = 2 is deemed

large, then the initial rejection is insensitive to the unobserved difference.

The relevant distribution (R+ or R−) to use for calculating the bound in the sensitivity

analysis indicates the possible direction of selection bias that could undermine an initial

significant finding of treatment effect. If the finding is a significantly positive effect, then

we only need to worry about the ‘positive’ selection problem, where a subject with a higher

potential treatment effect is also more likely to be treated; thus, the relevant distribution

is R+ that embodies selection bias in this direction. On the other hand, if the finding is a

significantly negative effect, then a reverse ‘negative’ selection problem, where a subject with

a lower potential treatment effect is also more likely to be treated, can weaken the original

finding, so the sensitivity analysis in the direction of R− is applicable.

4. DATA

Since our focus is on improving the estimation methodology in Rose (2004), we use the

original data set of Rose (2004) without further modifications or amendments.5 Rose (2004)

provides a detailed account of the construction of the data set.

The response variable yijt in our matching framework corresponds to the regressand in

the Rose’s (2004) gravity equation, which measures (the natural logarithm of) the average

value of real bilateral trade between countries i and j in year t. The treatment dummy

variable dijt corresponds to one of the three binary variables (Bothinijt, Oneinijt, GSPijt).

They measure, respectively, whether both countries i and j are GATT/WTO members in

year t, whether only one of the two countries (i, j) is a GATT/WTO member in year t, and

whether country i is a GSP beneficiary of country j or vice versa in year t.

The conditioning variables or covariates xijt in our matching framework correspond to the

complete list of regressors in Rose’s (2004) benchmark gravity equation. This includes: (1)

(the natural logarithm of) the distance between countries i and j; (2) (the natural logarithm

of) the product of real GDP’s of the country couple (i, j) in year t; (3) (the natural logarithm

of) the product of real per capita GDP’s of the country couple (i, j) in year t; (4) a binary

variable which indicates whether the country couple (i, j) share a common language; (5) a5The data set is available from Rose’s Web site (http://faculty.haas.berkeley.edu/arose/GATTdataStata.zip).

binary variable which indicates whether the country couple (i, j) share a land border; (6) a

discrete variable which counts the number of landlocked countries in the country couple (i, j);

(7) a discrete variable which counts the number of island nations in the country couple (i, j);

(8) (the natural logarithm of) the product of land areas of the country couple (i, j); (9) a

binary variable which indicates whether the country couple (i, j) were ever colonies after 1945

with the same colonizer; (10) a binary variable which indicates whether country i is a colony

of country j in year t or vice versa; (11) a binary variable which indicates whether country

i ever colonized country j or vice versa; (12) a binary variable which indicates whether the

country couple (i, j) remained part of the same nation during the sample; (13) a binary

variable which indicates whether the country couple (i, j) use the same currency in year t;

(14) a binary variable which indicates whether the country couple (i, j) belong to the same

regional trade agreement, (15) a list of year dummies for t = 1948, . . . , 1999; and (16) two

of the three binary variables (Bothin, Onein, GSP ), with the one whose treatment effect is

being investigated suitably excluded from the list.

The complete sample contains the above variables observed for 178 IMF trading entities

between 1948 and 1999 (with gaps). This amounts to a total of 234,597 observations.

5. ESTIMATION AND RESULTS

5.1 Matching Criteria and Procedures

We begin with the baseline methodology described in Section 3. This approach, by matching

in terms of the conditioning variables x, controls for the difference in bilateral trade arising

from differences in observable characteristics across country-couples and years (such as geo-

graphical proximity and output levels). Although the set of conditioning variables x used for

matching is quite extensive, it is possible that some systematic differences in unobservable

characteristics ε remain which lead to selection bias. The sensitivity analysis introduced in

Section 3.4 helps assess the sensitivity of estimation results to whatever selection bias may

remain; it, however, does not address the source of selection bias. We experiment with dif-

ferent matching criteria to address various potential selection biases. They are: matching

restricted to the observations of the same country-couple, matching restricted to the obser-

vations in the same year, matching restricted to the observations in the same GATT/WTO

period, and matching restricted to the observations of the same income-class combination

(details of the above criteria to be elaborated later). By restricting the potential match to

the observations of the specified criterion, we are accounting for the possibility that system-

atic unobservable differences exist (across country-couples, across years, across GATT/WTO

periods, or across income-class combinations) which influence bilateral trade patterns and

decisions to join the GATT/WTO or decisions to extend GSP. Tables 3–7 report the results

for each set of matching criterion.

For each set of matching criterion, we estimate the treatment effect of: ‘Both in GATT/WTO’,

‘One in GATT/WTO’, and ‘GSP’, respectively. For the GATT/WTO effect, both the effect

on the treated (i.e., those who chose to join the GATT/WTO) as well as the effect on the

untreated (i.e., those who chose not to join) are of interest. We report both effects and

the weighted average of them as the representative effect for all. For the GSP effect, we

report only the effect on the treated. We do not report the effect on the untreated, as GSP’s

are unilateral trade preferences extended only from the rich to the developing country. It

does not make much sense to propose a GSP arrangement between two rich countries, for

example, and to investigate the potential trade effect. On the other hand, the GSP effect

on the treated that we will report below should also be taken with a grain of salt, except

in the last matching exercise where matching is restricted to the observations of the same

income-class combination. This is because the decision to extend GSP’s and the bilateral

trade pattern may be both dependent on the relative income level of trading partners, which

poses potential selection bias problems. The last matching exercise, with matching restricted

to the observations of the same income-class combination, is least subject to this caveat.

When the treatment effect of ‘Both in GATT/WTO’ is investigated, observations with

only one country in the GATT/WTO are dropped. This leaves a remaining sample with

only observations where the two countries are either both in the GATT/WTO (114,750

observations) or both are outside the GATT/WTO (21,037 observations). Similarly, when the

treatment effect of ‘One in GATT/WTO’ is investigated, observations with both countries in

the GATT/WTO are dropped. The remaining sample thus includes only observations where

either only one of the two countries is in the GATT/WTO (98,810) or both are outside the

GATT/WTO (21,037). For the treatment effect of ‘GSP’, a small proportion (54,285) of the

whole sample (234,597) has GSP arrangements.

In all matching exercises, we restrict our attention to the case of pair-matching, in which

only one matched unit is selected. Since our conditioning variables x contain continuous

variables, the likelihood of two matched units having equal distance in terms of x from the

target is negligible and the case of multiple-matching can be safely ignored. In order to

measure the distance ‖xijt − xi′j′t′‖, we use the simple scale-normalized distance.

In Section 3.2, we introduced both simulation and normal approximation approaches to

obtaining the p-value of the treatment effect estimator D based on the permutation test.

Although not mentioned explicitly in Section 3.3, in addition to the normal approximation

approach, it is also possible to calculate the p-value for the signed-rank R statistic based on

simulated permutation samples. We carried out both approaches and found the normal p-

value to approximate the simulated p-value extremely well (which is expected as the sample

size is large). Thus, we present only the normal approximation result in the reports that

follow.

In any given matching exercise, we experiment with three caliper choices: the caliper is

set such that only 100%, 80%, or 60% of matched pairs are qualified for the estimation of the

treatment effect. For example, for the caliper choice of 60%, matched pairs with a distance

(in terms of x) exceeding the upper 60 percentile of all matched pairs are discarded. The

caliper choice of 100% is equivalent to using all available matched pairs.

5.2 Matching Results

In Tables 3–7, the first column ‘permutation test’ reports the results on permutation tests.

The ‘effect’ sub-column presents the treatment effect estimate based on the D statistic, the p-

value is obtained for the observed D statistic using the permutation test based on the normal

approximation approach, and the CI is obtained by inverting the test procedure. The second

column ‘signed-rank test’ reports the results on signed-rank tests. The ‘effect’ sub-column

presents the treatment effect estimate based on the Hodges and Lehmann (1963) estimator,

the p-value is obtained for the observed R statistic using the signed-rank test, and the CI is

obtained by inverting the test procedure. The third column ‘sensitivity analysis’ reports the

results on sensitivity analysis. The sensitivity analysis is conducted for the signed-rank test

based on a significance level of α = 0.05 in a one-sided or two-sided test. R+ or R− (as a

function of Γ) indicates the relevant distribution on which the bound for the p-value of the

signed-rank test is based. Γ∗ indicates the critical value of Γ at which the conclusion of the

signed-rank test reverses.

We discuss Tables 3–7 now. Table 3 reports the results of the baseline methodology,

labeled ‘unrestricted matching’. In this case, the pool of potential matches for an observation

are the observations with the opposite treatment; no further restriction is imposed. The

numbers of matched pairs obtained (M1 for the case of the effect on the treated, and M0 for

the untreated) are specified in the parentheses. We note that the permutation test and the

signed-rank test produce similar results. As the signed-rank test is considered more robust to

outliers and is also directly related to the sensitivity analysis, we cite the signed-rank test’s

figures below for illustrative purpose.

First, we note that the treatment effect of ‘Both in GATT/WTO’ on the treated is

large and significant. For example, with the 80% caliper, the point estimate indicates that

the GATT/WTO membership raises bilateral trade volume by 193% (= e1.075 − 1) if both

trading partners are GATT/WTO members. The corresponding effect is smaller at 76%

(= e0.568 − 1) if only one joins the GATT/WTO. Nevertheless, the effect is still positive and

significant. Thus, our estimation results suggest that the trade-creating effect of GATT/WTO

membership does not come at the cost of diverting trade from nonmembers. Relative to the

GATT/WTO membership, the preferential GSP scheme also promotes bilateral trade, by

a factor of 101% (= e0.696 − 1) with the 80% caliper, for trading relationships that apply

the scheme. It is important to note that the positive and stronger trade effect of ‘Both in

GATT/WTO’ is shared by a larger number of bilateral trading relationships (114, 750), than

the GSP scheme (54, 285). Thus, either on the average or in the aggregate, our estimation

results suggest that the realized trade-creating effect of GATT/WTO membership exceeds

that of GSP by a great extent.

How about the potential trade effect of GATT/WTO for trading relationships that are

outside the system? The treatment effect estimates on the untreated (with the 80% caliper)

suggest that the bilateral trade volume would have increased by 22% (= e0.200 − 1) if both

trading partners were to join the GATT/WTO or 9% (= e0.089−1) if only one of them did so.

The effects are smaller compared to the effect on the treated but they are still significantly

positive. As discussed in Section 3.1, the required assumption for applying the matching

estimator to the treated, y0 q d|x, is more likely to hold than to the untreated, y1 q d|x.

Thus, we will place less emphasis on the effect on the untreated in the following discussions,

although their results will continue to be reported in the tables.

Table 4 reports the results for ‘matching within country-couple’. In this case, the pool

of potential matches for an observation are restricted to the observations with the oppo-

site treatment and of the same country-couple. Some country-couples may be both in

the GATT/WTO, be both outside the GATT/WTO, or have only one of them in the

GATT/WTO, throughout the sampling years (1948 to 1999). Alternatively, some country-

couples may have only one of them in the GATT/WTO for some period of the sampling years

and then be both in the GATT/WTO throughout the rest of the sampling years. In these

cases, these observations do not have qualified matched controls (or matched treatment),

and are discarded from the sample. This explains the much smaller sample size shown in

Table 4. The estimated treatment effects on the treated for the three types of treatments

have the same ranking as in the case of unrestricted matching: Bothin effect > GSP effect

> Onein effect (with the 80% caliper). While the current estimates suggest overall smaller

treatment effects on the treated, the trade-creating effect if both trading partners are in the

GATT/WTO continues to be economically (and statistically) significant: for example, based

on the 80% caliper, bilateral trade increases by as much as 126% (= e0.814 − 1).

In Table 5, labeled ‘matching within year’, the pool of potential matches for an observation

are restricted to the observations with the opposite treatment and in the same year. In this

case, the year dummies in x are redundant and so are dropped from x. The estimation results

differ slightly from those of the ‘unrestricted matching’ in terms of the permutation test, but

they come across as almost the same as those in Table 3 in terms of the signed-rank test. This

indicates that in the case of ‘unrestricted matching’, the matched pairs often occur among

cross-section observations of the same year, and thus the estimates pick up mostly the cross-

section variations, whereas the estimates derived from ‘matching within country-couple’ as

discussed in the previous paragraph measure only time-series variations. Both cross-section

and time-series variations indicate that there are significant gains in trade by joining the

GATT/WTO.

Table 6 presents the results for ‘matching within period’. The pool of potential matches for

an observation are restricted to the observations with the opposite treatment and in the same

period, where the periods correspond to different eras of the GATT/WTO history. They are:

1948 (Before Annecy round), 1949-1951 (Annecy to Torquay round), 1952-1956 (Torquay to

Geneva round), 1957-1961 (Geneva to Dillon round), 1962-1967 (Dillon to Kennedy round),

1968-1979 (Kennedy to Tokyo round), 1980-1994 (Tokyo to Uruguay round), 1995-(After

Uruguay round). Given our earlier observations that in the case of ‘unrestricted matching’,

the matched pairs often occur among cross-section observations of the same year, it is no

surprise to see that the current estimation results again appear to be almost the same as in

the case of ‘unrestricted matching’, as the criterion of matching within the same period in

effect does not impose much extra restriction.

Table 7 reports the final set of results, for ‘matching within income-class combination’.

In this matching exercise, the pool of potential matches for an observation are restricted to

the observations with the opposite treatment and of the same income-class combination. The

income-class combinations are: ‘low income-low income’ country-couples, ‘low income-middle

income’ country couples, ‘low income-high income’ country couples, ‘middle income-middle

income’ country couples, ‘middle income-high income’ country couples, and ‘high income-

high income’ country couples. Observations without a qualified match are discarded. The

estimated treatment effects on the treated are overall smaller for GATT/WTO membership as

well as for GSP, although their relative ranking remains the same: Bothin effect > GSP effect

> Onein effect (with the 80% caliper), as with other matching criteria. The current estimates

suggest that the GATT/WTO membership promotes bilateral trade, by an economically and

statistically significant factor of: 108% (= e0.734 − 1) if both trading partners are in the

GATT/WTO and 58% (= e0.460−1) if only one of them is in the GATT/WTO. As discussed

earlier, the estimated GSP treatment effect with matching within the same income-class

combination is likely to be less subject to the selection bias problem. Based on this setup,

the GSP treatment effect is estimated to raise bilateral trade by a factor of 73% (= e0.551−1).

5.3 Sensitivity Analysis Results

How robust are the results we have referred to so far? By the sensitivity analysis, Table 3

indicates that in the case of ‘unrestricted matching’, the significant treatment effects of ‘Both

in GATT/WTO’ and ‘GSP’ are robust to any positive selection bias that leads to as much

as an odds ratio of 2.081, and 2.117 respectively, in receiving treatment between the treated

and untreated subject in any matched pair (by the 80% caliper and the two-sided test). On

the other hand, the robustness of the significant treatment effect of ‘One in GATT/WTO’

to potential positive selection bias is relatively weaker (measured by Γ∗ at 1.521). The same

degrees of robustness of the three treatments reappear in Tables 5 and 6, when the matching

is restricted to the observations in the same year, or in the same period.

Are these figures large enough? In using similar sensitivity analysis, Aakvik (2001) seems

to regard Γ = 1.5 ∼ 2 as large, while Hujer et al. (2004) appear to base their discussions

on lower numbers of Γ = 1.25 ∼ 1.5. Given that the list of conditioning variables x used

in our framework is extensive and includes most of the important variables likely to affect

bilateral trade flows, we feel that Γ∗ > 2 is sufficiently large. In other words, we judge that

any important omitted variables in ε are not likely to result in as much as an odds ratio of 2

in receiving treatment between the treated and untreated subject in any matched pair. Thus,

we may accept these estimated treatment effects of ‘Both in GATT/WTO’ and ‘GSP’ with

a reasonable degree of confidence.

When the matching criterion becomes more stringent such that further imaginable sources

of selection bias are minimized, one may accept an even lower magnitude of Γ∗, as the

remaining possibility of selection bias is lower. Both the ‘matching within country-couple’

and the ‘matching within income-class combination’ impose effective extra constraints relative

to the ‘unrestricted matching’ benchmark, as discussed earlier and to some extent indicated

by their fewer effective matched pairs. In the latter case of ‘matching within income-class

combination’, the robustness of the treatment effect estimate is lower in general than the

benchmark. The tolerance threshold (Γ∗) for positive selection bias now stands at 1.601,

1.807, and 1.391 (by the 80% caliper and the two-sided test) for the estimated treatment

effect of ‘Both in GATT/WTO’, ‘GSP’, and ‘One in GATT/WTO’, respectively. It will take

further investigations to make a fine judgement of whether the much lower thresholds of 1.601

and 1.391 are acceptable given the stricter criterion of matching within the same income-class

combination. However, the treatment effect estimate of GSP may be regarded as reasonably

robust with a tolerance level of Γ∗ = 1.807 in the current stringent matching setup.

On the other hand, with the more stringent criterion of ‘matching within country-couple’,

the robustness of the estimated treatment effects actually strengthens (as illustrated in Ta-

ble 4). It now takes a strong presence of positive selection bias that leads to as much as

an odds ratio of 2.543 (by the 80% caliper and the two-sided test), in receiving treatment

between the treated and untreated subject in any matched pair, to nullify the original signifi-

cance finding of ‘Both in GATT/WTO’ treatment effect. The corresponding figures are 2.494

and 1.772 for the ‘GSP’ and ‘One in GATT/WTO’ treatment, respectively. Thus, relative

to the ‘unrestricted matching’ benchmark, it is even more comfortable for us to accept the

results on the Bothin and the GSP treatment effects, as the degree of tolerance level for

selection bias is higher despite that the possibility of remaining selection bias is lower with

the extra matching criterion.

5.4 Overall Results

Overall, we conclude with two sets of relatively robust estimates for the trade effect of

GATT/WTO membership, represented by the Bothin treatment effect obtained by ‘un-

restricted matching’ and by ‘matching within country-couple’. As discussed earlier, the re-

sults of ‘unrestricted matching’ are almost identical to those of ‘matching within year’ and

‘matching within period’ and capture most likely the cross-sectional treatment effect. Our

intermediate estimate (by the 80% caliper) suggests that the GATT/WTO membership in-

creases bilateral trade volume by 193% (= e1.075 − 1) for trading partners that are both

GATT/WTO members, relative to trading partners that are both outside the GATT/WTO.

On the other hand, the results of ‘matching within country-couple’ capture the time-series

variation of treatment effect. In this case, our intermediate estimate (by the 80% caliper)

suggests that the GATT/WTO membership increases bilateral trade volume by a smaller

factor of 126% (= e0.814− 1) when trading partners both join GATT/WTO, relative to when

they both do not.

Regarding GSP, we are more comfortable with the results obtained based on ‘matching

within income-class combination’, as the decision to extend GSP is very likely to be dependent

on trading partners’ relative income levels. The intermediate estimate (by the 80% caliper)

suggests that the GSP scheme raises bilateral trade volume by a factor of 73% (= e0.551− 1).

Note again that the GATT/WTO effect has in the past applied to a much larger number

of trading relationships (114,750) than the GSP effect (54,285). Thus, either on the average

or in the aggregate, the realized trade promoting effect of GATT/WTO far exceeds that of

6. CONCLUSION

As the multilateral trade institution evolved from the simple trade treaty, the GATT, to the

overarching organization, the WTO, it is timely to review whether the institution lives up

to its objective of promoting international trade. In spite of the common affirmative im-

pression, Rose (2004) argues that little evidence is found that the GATT/WTO has had an

impact on trade. In this paper, we readdress this important policy question, arguing against

the parametric gravity-equation approach used by Rose (2004), and propose nonparametric

approaches to estimating the GATT/WTO trade effect. This involves using matching meth-

ods to estimate the ‘treatment effect’ of GATT/WTO membership and permutation-based

inferential procedures to assess statistical significance of the estimated effects. The problem

of potential selection bias is addressed by the Rosenbaum (2002) sensitivity analysis and by

restricting matching within sub-samples.

Contrary to Rose (2004), we find consistent and large positive effects on trade when

countries participate in the GATT/WTO system. The effect is larger when two countries in

a bilateral trade relationship are both members than when only one is a member, but the

effect is nonetheless significantly positive even when only one is a member, confirming an

overall trade-creating effect of the multilateral institution. The positive effect of multilateral

participation in the GATT/WTO system also exceeds that of the preferential GSP scheme by

a great extent, either on the average or in the aggregate, contrasting Rose’s (2004) result that

GSP is more effective in promoting trade than the GATT/WTO. Overall, our finding confirms

the common sense that preferential liberalizations (via GSP or unilateral participation in the

GATT/WTO) may be good, but multilateral liberalizations (via reciprocal participation in

the GATT/WTO) are most effective at promoting trade.

We conclude with some qualifications of our findings. First, the data set of Rose (2004)

that we use includes only observations with positive bilateral trade flows. A recent study by

Felbermayr and Kohler (2007) suggests that by taking into account trading relationships with

zero trade leads to a bigger trade effect of GATT/WTO membership than indicated by Rose

(2004). This finding does not undermine our foregoing conclusions, if we accept the notion

proposed in Felbermayr and Kohler (2007) that non-existent trading relationships are also

more likely those of non-participants in the GATT/WTO. It implies that if we already find

significantly positive trade effect of GATT/WTO conditional on observations with positive

trade flows, then the ultimate trade effect of GATT/WTO incorporating the extensive margin

would only be larger. Second, using the data set of Rose (2004), which compiles the average

of export and import flows, implies that we can not differentiate the direction of trade flows

and thus control for exporter or importer specific effects. However, just as in Rose (2004),

who controls for country-couple or dyad specific effect in some analysis with fixed-effect

estimator, we accomplish the same by restricting matching to between observations of the

same country-couple in one of our analysis. It may be helpful to further verify our findings

by using directional trade data. We leave this for future research.

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Table 1: misspecification test of the gravity equation(I) Rose (II) RESET (III) with interaction terms

Both in GATT/WTO -0.04 (0.05) -0.04 (0.05) -10.72 (1.10)One in GATT/WTO -0.06 (0.05) -0.07 (0.05) -7.61 (1.08)GSP 0.86 (0.03) 0.99 (0.04) 0.56 (0.26)Log distance -1.12 (0.02) -1.33 (0.05) -1.10 (0.06)Log product real GDP 0.92 (0.01) 1.08 (0.03) 0.86 (0.03)Log product real GDP p/c 0.32 (0.01) 0.38 (0.02) 0.05 (0.04)Regional FTA 1.20 (0.11) 1.55 (0.11) 0.58 (0.39)Currency union 1.12 (0.12) 1.30 (0.13) 0.04 (0.32)Common Language 0.31 (0.04) 0.35 (0.04) 0.09 (0.11)Land border 0.53 (0.11) 0.67 (0.11) 0.56 (0.19)Number landlocked -0.27 (0.03) -0.31 (0.03) -0.17 (0.09)Number islands 0.04 (0.04) 0.06 (0.04) 0.11 (0.12)Log product land area -0.10 (0.01) -0.11 (0.01) -0.17 (0.02)Common colonizer 0.58 (0.07) 0.69 (0.07) 1.08 (0.16)Currently colonized 1.08 (0.23) 1.28 (0.23) 4.81 (0.57)Ever colony 1.16 (0.12) 1.45 (0.13) -0.53 (0.21)Common country -0.02 (1.08) -0.08 (1.07) 0.05 (1.03)

( Log real trade)2 -0.01 (0.002)Both in x GSP 0.11 (0.26)Both in x Log distance -0.03 (0.07)Both in x Log product real GDP 0.07 (0.03)Both in x Log product real GDP p/c 0.33 (0.05)Both in x Regional FTA 0.27 (0.41)Both in x Currency union 1.37 (0.35)Both in x Common Language 0.30 (0.12)Both in x Land border 0.02 (0.25)Both in x Number landlocked -0.13 (0.09)Both in x Number islands -0.10 (0.12)Both in x Log product land area 0.10 (0.02)Both in x Common colonizer -0.61 (0.18)Both in x Currently colonized -3.91 (0.62)Both in x Ever colony 1.69 (0.25)Both in x Common country (dropped)One in x GSP 0.48 (0.26)One in x Log distance -0.01 (0.06)One in x Log product real GDP 0.05 (0.03)One in x Log product real GDP p/c 0.25 (0.05)One in x Regional FTA 1.17 (0.41)One in x Currency union 0.67 (0.37)One in x Common Language 0.27 (0.12)One in x Land border -0.08 (0.23)One in x Number landlocked -0.10 (0.09)One in x Number islands -0.10 (0.12)One in x Log product land area 0.06 (0.02)One in x Common colonizer -0.58 (0.17)One in x Currently colonized (dropped)One in x Ever colony 1.71 (0.24)One in x Common country (dropped)

Observations 234,597 234,597 234,597R2 0.6480 0.6486 0.6525RMSE 1.9796 1.9777 1.9669

Note:Regressand: log real trade. OLS with year effects (intercepts not reported). Robust standard errors (clustering bycountry-couples) are in parentheses.

Table 2: trade effect based on gravity equation with interaction termsBoth in Effect One in Effect

PercentilesSmallest -3.2530 -2.551725% -0.2579 -0.209650% 0.2552 0.209375% 0.7786 0.7118Largest 4.8556 4.8237

Mean 0.2724 0.2723Standard Error of Mean 0.0017 0.0015Observations 234,597 234,597

Standard Deviation 0.8428 0.7442Variance 0.7103 0.5538Skewness 0.3219 0.6496Kurtosis 3.9576 4.4601

Note:Calculation based on regression (III) of Table 1. For tradingpartners i and j in year t,(i) {Both in effect}ijt = β{Both in} + β{Both in x GSP}{GSP}ijt + . . . + β{Both in x Ever colony} {Ever colony}ijt;(ii) {One in effect}ijt = β{One in} + β{One in x GSP} {GSP}ijt

+ . . . + β{One in x Common colonizer} {Common colonizer}ijt +β{One in x Ever colony} {Ever colony}ijt.

Table 3: treatment effect – unrestricted matchingpermutation test signed-rank test sensitivity analysis

one-sided test two-sided testcaliper effect p-value 95% CI effect p-value 95% CI Γ∗ as in Γ∗ as in

Both in GATT/WTO treatment effecton the treated (M1 = 114, 750):100% 1.328 0.000 [1.307, 1.349] 1.332 0.000 [1.312, 1.351] 2.434 R+ 2.428 R+

80% 1.075 0.000 [1.052, 1.098] 1.075 0.000 [1.053, 1.096] 2.086 R+ 2.081 R+

60% 0.836 0.000 [0.810, 0.862] 0.835 0.000 [0.810, 0.859] 1.780 R+ 1.775 R+

on the untreated (M0 = 21, 037):100% 0.337 0.000 [0.296, 0.379] 0.303 0.000 [0.266, 0.342] 1.250 R+ 1.243 R+

80% 0.239 0.000 [0.192, 0.286] 0.200 0.000 [0.157, 0.241] 1.144 R+ 1.138 R+

60% 0.185 0.000 [0.131, 0.239] 0.138 0.000 [0.090, 0.187] 1.084 R+ 1.077 R+

on all (M1 + M0 = 135, 787):100% 1.175 0.000 [1.156, 1.193] 1.161 0.000 [1.143, 1.179] 2.209 R+ 2.205 R+

80% 0.899 0.000 [0.878, 0.919] 0.883 0.000 [0.863, 0.902] 1.858 R+ 1.854 R+

60% 0.636 0.000 [0.613, 0.659] 0.619 0.000 [0.597, 0.640] 1.559 R+ 1.555 R+

One in GATT/WTO treatment effecton the treated (M1 = 98, 810):100% 0.767 0.000 [0.746, 0.789] 0.773 0.000 [0.753, 0.792] 1.759 R+ 1.755 R+

80% 0.564 0.000 [0.540, 0.588] 0.568 0.000 [0.547, 0.589] 1.525 R+ 1.521 R+

60% 0.422 0.000 [0.396, 0.449] 0.428 0.000 [0.405, 0.451] 1.397 R+ 1.393 R+

on the untreated (M0 = 21, 037):100% 0.030 0.068 [-0.009, 0.069] 0.034 0.022 [0.000, 0.068] 1.006 R+ 1.001 R+

80% 0.092 0.000 [0.048, 0.135] 0.089 0.000 [0.052, 0.126] 1.057 R+ 1.051 R+

60% 0.078 0.001 [0.028, 0.129] 0.084 0.000 [0.041, 0.127] 1.046 R+ 1.039 R+

on all (M1 + M0 = 119, 847):100% 0.638 0.000 [0.619, 0.657] 0.632 0.000 [0.615, 0.649] 1.610 R+ 1.607 R+

80% 0.443 0.000 [0.422, 0.464] 0.437 0.000 [0.418, 0.455] 1.401 R+ 1.397 R+

60% 0.324 0.000 [0.301, 0.347] 0.321 0.000 [0.301, 0.340] 1.297 R+ 1.293 R+

GSP treatment effecton the treated (M1 = 54, 285):100% 0.851 0.000 [0.831, 0.871] 0.792 0.000 [0.774, 0.811] 2.277 R+ 2.269 R+

80% 0.757 0.000 [0.736, 0.778] 0.696 0.000 [0.676, 0.716] 2.125 R+ 2.117 R+

60% 0.693 0.000 [0.668, 0.717] 0.627 0.000 [0.604, 0.649] 1.998 R+ 1.990 R+

Note:1. The pool of potential matches for an observation are observations with the opposite treatment; no further restrictionis imposed. The numbers of matched pairs obtained (M1 for the case of the effect on the treated, and M0 for theuntreated) are specified in the parentheses.2. The caliper choice is set such that only 100%, 80%, or 60% of matched pairs are qualified for the estimation of thetreatment effect. For example, for the case of 60%, matched pairs with a distance in terms of x exceeding the upper 60percentile of all matched pairs are discarded.3. The regressors in the benchmark gravity equation of Rose (2004) are used as the conditioning variables x for matching,with the treatment dummy variable being investigated (Bothin, Onein, or GSP ) suitably excluded from the list.4. In the column ‘permutation test’, the ‘effect’ sub-column presents the treatment effect estimate based on theD statistic; the p-value is obtained for the observed D statistic using the permutation test based on the normalapproximation approach; the CI is obtained by inverting the test procedure as discussed in the main text.5. In the column ‘signed-rank test’, the ‘effect’ sub-column presents the treatment effect estimate based on the Hodgesand Lehmann (1963) estimator; the p-value is obtained for the observed R statistic using the signed-rank test based onthe normal approximation approach; the CI is obtained by inverting the test procedure as discussed in the main text.6. In the column ‘sensitivity analysis’, the sensitivity analysis is conducted for the above signed-rank test based on asignificance level of α = 0.05 in a one-sided or two-sided test. R+ or R− (as a function of Γ) indicates the relevantdistribution on which the bound for the p-value of the signed-rank test is based. Γ∗ indicates the critical value of Γ atwhich the conclusion of the signed-rank test reverses.

Table 4: treatment effect – matching within country-couplepermutation test signed-rank test sensitivity analysis

80% 0.760 0.000 [0.727, 0.792] 0.814 0.000 [0.785, 0.844] 2.559 R+ 2.543 R+

60% 0.833 0.000 [0.797, 0.870] 0.876 0.000 [0.843, 0.910] 2.792 R+ 2.771 R+

80% 1.117 0.000 [1.067, 1.167] 1.161 0.000 [1.115, 1.207] 3.475 R+ 3.440 R+

60% 0.989 0.000 [0.931, 1.048] 1.019 0.000 [0.967, 1.071] 3.017 R+ 2.983 R+

on all (M1 + M0 = 29, 270):100% 1.058 0.000 [1.033, 1.082] 1.110 0.000 [1.087, 1.132] 3.515 R+ 3.496 R+

80% 0.895 0.000 [0.868, 0.923] 0.943 0.000 [0.918, 0.967] 2.927 R+ 2.911 R+

60% 0.935 0.000 [0.903, 0.967] 0.969 0.000 [0.940, 0.998] 3.021 R+ 3.002 R+

80% 0.403 0.000 [0.374, 0.432] 0.470 0.000 [0.444, 0.495] 1.782 R+ 1.772 R+

60% 0.371 0.000 [0.335, 0.407] 0.460 0.000 [0.428, 0.491] 1.666 R+ 1.656 R+

80% 0.463 0.000 [0.423, 0.503] 0.525 0.000 [0.492, 0.559] 1.818 R+ 1.805 R+

60% 0.386 0.000 [0.339, 0.432] 0.430 0.000 [0.390, 0.469] 1.610 R+ 1.597 R+

on all (M1 + M0 = 38, 645):100% 0.509 0.000 [0.488, 0.529] 0.574 0.000 [0.556, 0.592] 2.023 R+ 2.016 R+

80% 0.428 0.000 [0.404, 0.452] 0.492 0.000 [0.472, 0.513] 1.816 R+ 1.808 R+

60% 0.403 0.000 [0.374, 0.432] 0.478 0.000 [0.453, 0.503] 1.706 R+ 1.698 R+

80% 0.492 0.000 [0.479, 0.506] 0.489 0.000 [0.478, 0.501] 2.504 R+ 2.494 R+

60% 0.379 0.000 [0.363, 0.395] 0.371 0.000 [0.357, 0.385] 1.945 R+ 1.937 R+

Note:1. The pool of potential matches for an observation are restricted to observations with the opposite treatment and ofthe same country-couple; observations without a match are discarded. The numbers of matched pairs obtained (M1 forthe case of the effect on the treated, and M0 for the untreated) are specified in the parentheses.2. The caliper choice is set such that only 100%, 80%, or 60% of matched pairs are qualified for the estimation of thetreatment effect. For example, for the case of 60%, matched pairs with a distance in terms of x exceeding the upper 60percentile of all matched pairs are discarded.3. The regressors in the benchmark gravity equation of Rose (2004) are used as the conditioning variables x for matching,with the treatment dummy variable being investigated (Bothin, Onein, or GSP ) suitably excluded from the list.4. In the column ‘permutation test’, the ‘effect’ sub-column presents the treatment effect estimate based on theD statistic; the p-value is obtained for the observed D statistic using the permutation test based on the normalapproximation approach; the CI is obtained by inverting the test procedure as discussed in the main text.5. In the column ‘signed-rank test’, the ‘effect’ sub-column presents the treatment effect estimate based on the Hodgesand Lehmann (1963) estimator; the p-value is obtained for the observed R statistic using the signed-rank test based onthe normal approximation approach; the CI is obtained by inverting the test procedure as discussed in the main text.6. In the column ‘sensitivity analysis’, the sensitivity analysis is conducted for the above signed-rank test based on asignificance level of α = 0.05 in a one-sided or two-sided test. R+ or R− (as a function of Γ) indicates the relevantdistribution on which the bound for the p-value of the signed-rank test is based. Γ∗ indicates the critical value of Γ atwhich the conclusion of the signed-rank test reverses.

Table 5: treatment effect – matching within yearpermutation test signed-rank test sensitivity analysis

80% 1.075 0.000 [1.052, 1.098] 1.075 0.000 [1.053, 1.096] 2.086 R+ 2.081 R+

60% 0.836 0.000 [0.810, 0.862] 0.835 0.000 [0.810, 0.859] 1.780 R+ 1.775 R+

80% 0.239 0.000 [0.192, 0.286] 0.200 0.000 [0.157, 0.241] 1.144 R+ 1.138 R+

60% 0.185 0.000 [0.131, 0.239] 0.138 0.000 [0.090, 0.187] 1.084 R+ 1.077 R+

on all (M1 + M0 = 135, 787):100% 1.176 0.000 [1.157, 1.194] 1.164 0.000 [1.146, 1.181] 2.209 R+ 2.205 R+

80% 0.899 0.000 [0.878, 0.919] 0.883 0.000 [0.863, 0.902] 1.858 R+ 1.854 R+

60% 0.636 0.000 [0.613, 0.659] 0.619 0.000 [0.597, 0.640] 1.559 R+ 1.555 R+

80% 0.564 0.000 [0.540, 0.588] 0.568 0.000 [0.547, 0.589] 1.525 R+ 1.521 R+

60% 0.422 0.000 [0.396, 0.449] 0.428 0.000 [0.405, 0.451] 1.397 R+ 1.393 R+

80% 0.092 0.000 [0.048, 0.135] 0.089 0.000 [0.052, 0.126] 1.057 R+ 1.051 R+

60% 0.078 0.001 [0.028, 0.129] 0.084 0.000 [0.041, 0.127] 1.046 R+ 1.039 R+

on all (M1 + M0 = 119, 847):100% 0.633 0.000 [0.614, 0.652] 0.628 0.000 [0.611, 0.645] 1.605 R+ 1.601 R+

80% 0.443 0.000 [0.422, 0.464] 0.437 0.000 [0.418, 0.455] 1.401 R+ 1.397 R+

60% 0.324 0.000 [0.301, 0.347] 0.321 0.000 [0.301, 0.340] 1.297 R+ 1.293 R+

80% 0.757 0.000 [0.736, 0.778] 0.696 0.000 [0.676, 0.716] 2.125 R+ 2.117 R+

60% 0.693 0.000 [0.668, 0.717] 0.627 0.000 [0.604, 0.649] 1.998 R+ 1.990 R+

Note:1. The pool of potential matches for an observation are restricted to observations with the opposite treatment and ofthe same year; observations without a match are discarded. The numbers of matched pairs obtained (M1 for the caseof the effect on the treated, and M0 for the untreated) are specified in the parentheses.2. The caliper choice is set such that only 100%, 80%, or 60% of matched pairs are qualified for the estimation of thetreatment effect. For example, for the case of 60%, matched pairs with a distance in terms of x exceeding the upper 60percentile of all matched pairs are discarded.3. The regressors in the benchmark gravity equation of Rose (2004) are used as the conditioning variables x formatching, with the year dummies and the treatment dummy variable being investigated (Bothin, Onein, or GSP )suitably excluded from the list.4. In the column ‘permutation test’, the ‘effect’ sub-column presents the treatment effect estimate based on theD statistic; the p-value is obtained for the observed D statistic using the permutation test based on the normalapproximation approach; the CI is obtained by inverting the test procedure as discussed in the main text.5. In the column ‘signed-rank test’, the ‘effect’ sub-column presents the treatment effect estimate based on the Hodgesand Lehmann (1963) estimator; the p-value is obtained for the observed R statistic using the signed-rank test based onthe normal approximation approach; the CI is obtained by inverting the test procedure as discussed in the main text.6. In the column ‘sensitivity analysis’, the sensitivity analysis is conducted for the above signed-rank test based on asignificance level of α = 0.05 in a one-sided or two-sided test. R+ or R− (as a function of Γ) indicates the relevantdistribution on which the bound for the p-value of the signed-rank test is based. Γ∗ indicates the critical value of Γ atwhich the conclusion of the signed-rank test reverses.

Table 6: treatment effect – matching within periodpermutation test signed-rank test sensitivity analysis

80% 1.075 0.000 [1.052, 1.098] 1.075 0.000 [1.053, 1.096] 2.086 R+ 2.081 R+

60% 0.836 0.000 [0.810, 0.862] 0.835 0.000 [0.810, 0.859] 1.780 R+ 1.775 R+

80% 0.239 0.000 [0.192, 0.286] 0.200 0.000 [0.157, 0.241] 1.144 R+ 1.138 R+

60% 0.185 0.000 [0.131, 0.239] 0.138 0.000 [0.090, 0.187] 1.084 R+ 1.077 R+

on all (M1 + M0 = 135, 787):100% 1.177 0.000 [1.158, 1.196] 1.165 0.000 [1.147, 1.183] 2.213 R+ 2.208 R+

80% 0.899 0.000 [0.878, 0.919] 0.883 0.000 [0.863, 0.902] 1.858 R+ 1.854 R+

60% 0.636 0.000 [0.613, 0.659] 0.619 0.000 [0.597, 0.640] 1.559 R+ 1.555 R+

80% 0.564 0.000 [0.540, 0.588] 0.568 0.000 [0.547, 0.589] 1.525 R+ 1.521 R+

60% 0.422 0.000 [0.396, 0.449] 0.428 0.000 [0.405, 0.451] 1.397 R+ 1.393 R+

80% 0.092 0.000 [0.048, 0.135] 0.089 0.000 [0.052, 0.126] 1.057 R+ 1.051 R+

60% 0.078 0.001 [0.028, 0.129] 0.084 0.000 [0.041, 0.127] 1.046 R+ 1.039 R+

on all (M1 + M0 = 119, 847):100% 0.634 0.000 [0.615, 0.653] 0.629 0.000 [0.612, 0.646] 1.606 R+ 1.603 R+

80% 0.443 0.000 [0.422, 0.464] 0.437 0.000 [0.418, 0.455] 1.401 R+ 1.397 R+

60% 0.324 0.000 [0.301, 0.347] 0.321 0.000 [0.301, 0.340] 1.297 R+ 1.293 R+

80% 0.757 0.000 [0.736, 0.778] 0.696 0.000 [0.676, 0.716] 2.125 R+ 2.117 R+

60% 0.693 0.000 [0.668, 0.717] 0.627 0.000 [0.604, 0.649] 1.998 R+ 1.990 R+

Note:1. The pool of potential matches for an observation are restricted to observations with the opposite treatment and ofthe same period, where the periods are: 1948 (Before Annecy round), 1949-1951 (Annecy to Torquay round), 1952-1956(Torquay to Geneva round), 1957-1961 (Geneva to Dillon round), 1962-1967 (Dillon to Kennedy round), 1968-1979(Kennedy to Tokyo round), 1980-1994 (Tokyo to Uruguay round), 1995-(After Uruguay round). Observations withouta match are discarded. The numbers of matched pairs obtained (M1 for the case of the effect on the treated, and M0

for the untreated) are specified in the parentheses.2. The caliper choice is set such that only 100%, 80%, or 60% of matched pairs are qualified for the estimation of thetreatment effect. For example, for the case of 60%, matched pairs with a distance in terms of x exceeding the upper 60percentile of all matched pairs are discarded.3. The regressors in the benchmark gravity equation of Rose (2004) are used as the conditioning variables x for matching,with the treatment dummy variable being investigated (Bothin, Onein, or GSP ) suitably excluded from the list.4. In the column ‘permutation test’, the ‘effect’ sub-column presents the treatment effect estimate based on theD statistic; the p-value is obtained for the observed D statistic using the permutation test based on the normalapproximation approach; the CI is obtained by inverting the test procedure as discussed in the main text.5. In the column ‘signed-rank test’, the ‘effect’ sub-column presents the treatment effect estimate based on the Hodgesand Lehmann (1963) estimator; the p-value is obtained for the observed R statistic using the signed-rank test based onthe normal approximation approach; the CI is obtained by inverting the test procedure as discussed in the main text.6. In the column ‘sensitivity analysis’, the sensitivity analysis is conducted for the above signed-rank test based on asignificance level of α = 0.05 in a one-sided or two-sided test. R+ or R− (as a function of Γ) indicates the relevantdistribution on which the bound for the p-value of the signed-rank test is based. Γ∗ indicates the critical value of Γ atwhich the conclusion of the signed-rank test reverses.

Table 7: treatment effect – matching within income-class combinationpermutation test signed-rank test sensitivity analysis

80% 0.778 0.000 [0.753, 0.802] 0.734 0.000 [0.711, 0.757] 1.605 R+ 1.601 R+

60% 0.541 0.000 [0.514, 0.569] 0.504 0.000 [0.478, 0.530] 1.389 R+ 1.385 R+

80% 0.175 0.000 [0.128, 0.222] 0.131 0.000 [0.089, 0.173] 1.083 R+ 1.077 R+

60% 0.101 0.000 [0.047, 0.155] 0.059 0.008 [0.010, 0.107] 1.015 R+ 1.009 R+

on all (M1 + M0 = 133, 972):100% 0.997 0.000 [0.977, 1.016] 0.955 0.000 [0.936, 0.973] 1.883 R+ 1.880 R+

80% 0.662 0.000 [0.640, 0.684] 0.612 0.000 [0.592, 0.633] 1.507 R+ 1.504 R+

60% 0.442 0.000 [0.418, 0.467] 0.402 0.000 [0.379, 0.424] 1.313 R+ 1.309 R+

80% 0.476 0.000 [0.452, 0.500] 0.460 0.000 [0.438, 0.481] 1.394 R+ 1.391 R+

60% 0.342 0.000 [0.315, 0.370] 0.324 0.000 [0.300, 0.347] 1.267 R+ 1.263 R+

80% 0.063 0.002 [0.020, 0.105] 0.051 0.003 [0.014, 0.087] 1.020 R+ 1.014 R+

60% 0.034 0.084 [-0.014, 0.083] 0.028 0.092 [-0.012, 0.070] 1.007 R− 1.013 R−on all (M1 + M0 = 119, 376):100% 0.544 0.000 [0.524, 0.563] 0.512 0.000 [0.495, 0.530] 1.455 R+ 1.452 R+

80% 0.391 0.000 [0.369, 0.412] 0.369 0.000 [0.350, 0.388] 1.320 R+ 1.316 R+

60% 0.215 0.000 [0.192, 0.239] 0.200 0.000 [0.179, 0.219] 1.164 R+ 1.161 R+

80% 0.588 0.000 [0.567, 0.608] 0.551 0.000 [0.531, 0.570] 1.813 R+ 1.807 R+

60% 0.507 0.000 [0.485, 0.530] 0.474 0.000 [0.452, 0.496] 1.706 R+ 1.699 R+

Note:1. The pool of potential matches for an observation are restricted to observations with the opposite treatment andof the same income-class combination, where the income-class combinations are: ‘low income-low income’ country-couples, ‘low income-middle income’ country couples, ‘low income-high income’ country couples, ‘middle income-middleincome’ country couples, ‘middle income-high income’ country couples, and ‘high income-high income’ country couples.Observations without a match are discarded. The numbers of matched pairs obtained (M1 for the case of the effect onthe treated, and M0 for the untreated) are specified in the parentheses.2. The caliper choice is set such that only 100%, 80%, or 60% of matched pairs are qualified for the estimation of thetreatment effect. For example, for the case of 60%, matched pairs with a distance in terms of x exceeding the upper 60percentile of all matched pairs are discarded.3. The regressors in the benchmark gravity equation of Rose (2004) are used as the conditioning variables x for matching,with the treatment dummy variable being investigated (Bothin, Onein, or GSP ) suitably excluded from the list.4. In the column ‘permutation test’, the ‘effect’ sub-column presents the treatment effect estimate based on theD statistic; the p-value is obtained for the observed D statistic using the permutation test based on the normalapproximation approach; the CI is obtained by inverting the test procedure as discussed in the main text.5. In the column ‘signed-rank test’, the ‘effect’ sub-column presents the treatment effect estimate based on the Hodgesand Lehmann (1963) estimator; the p-value is obtained for the observed R statistic using the signed-rank test based onthe normal approximation approach; the CI is obtained by inverting the test procedure as discussed in the main text.6. In the column ‘sensitivity analysis’, the sensitivity analysis is conducted for the above signed-rank test based on asignificance level of α = 0.05 in a one-sided or two-sided test. R+ or R− (as a function of Γ) indicates the relevantdistribution on which the bound for the p-value of the signed-rank test is based. Γ∗ indicates the critical value of Γ atwhich the conclusion of the signed-rank test reverses.

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